Due to the limited power cell performance of battery electric vehicles (BEVs), BEV drivers endure a short cruising range and a long charging time. Additionally, uneven charging facilities and unreasonable charging arrangements result in partial queuing and partial idling of charging stations. To solve these problems, it is critical to understand BEV charging behavior and its influential factors. Considering the urgency of BEV charging, BEV drivers tend to choose fast charging when BEV is in driving state. This study investigates fast charging behavior by utilizing private BEV connected data collected from Beijing. First, 130 private BEVs with travel rules were screened out. Using seven months of BEV data, a total of 15,752 trajectories were identified, among which 2161 have fast charging behavior. According to the relationship between fast charging behavior and some influential factors, including battery modeling, driving behavior, weather and environment, and even user habit, were empirically investigated. Moreover, the battery state of charge at the start time, time-origin, travel time duration, driving distance, driving speed, wind power, temperature, and last-fast-status are determined as significant influencing factors. Lastly, a prediction model based on the significant factors is proposed to estimate whether there is fast charging in a day trajectory. The proposed model achieves the best accuracy over compared models, i.e., univariate linear regression (ULR) with several factors and multivariate linear regression (MLR) model. The study is expected to help better understand fast charging behavior and further contribute to the future improvement of fast charging efficiency.